Geodesic
Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 73-77

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An exponential queuing network containing nodes of two types — single-line and multi-line is considered. In contrast to Jackson networks, the sojourn time at the nodes of the network is a random variable, the conditional distribution of which is exponential for a fixed number of claims in the node. For single-line nodes, the routing matrices of the served and non-served customers are, generally speaking, different, and for multi-line nodes they coincide. A sufficient ergodicity condition is established and a stationary distribution is found.
Keywords: open queuing network, single-line and multi-line nodes, limited sojourn time, ergodicity condition, stationary distribution. 
@article{PFMT_2020_3_a11,
     author = {Yu. V. Malinkovskii and V. A. Niamilastsivaya},
     title = {Stationary distribution of {Jackson} networks with an exponential constraint on the sojourn time of claims},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {73--77},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/}
}
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Yu. V. Malinkovskii; V. A. Niamilastsivaya. Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 73-77. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/